Friend,
If you see the LSA details you will find something like a advertising router field.
SO when a DR sends a packet it would set the advertising router field to be the IP of the router advertising that LSA. This way it would come to know the nexthop router
Eg..see the 20.20.20.0 network is not advertised by DR but another router in the broadcast network
LS age: 369
Options: (No TOS-capability, DC)
LS Type: Router Links
Link State ID: 10.10.10.1
Advertising Router: 10.10.10.1
LS Seq Number: 80000005
Checksum: 0x5014
Length: 48
Number of Links: 2
Link connected to: a Stub Network
(Link ID) Network/subnet number: 20.20.20.0
(Link Data) Network Mask: 255.255.255.0
Number of TOS metrics: 0
TOS 0 Metrics: 1
Link connected to: a Transit Network
(Link ID) Designated Router address: 10.10.10.2
(Link Data) Router Interface address: 10.10.10.1
Number of TOS metrics: 0
HTH, rate if it does
Narayan